Apparatus and method for noise attenuation in a speech recognition system

ABSTRACT

The noise suppressor utilizes statistical characteristics of the noise signal to attenuate amplitude values of the noisy speech signal that have a probability of containing noise. In one embodiment, the noise suppressor utilizes an attenuation function having a shape determined in part by a noise average and a noise standard deviation. In a further embodiment, the noise suppressor also utilizes an adaptive attenuation coefficient that depends on signal-to-noise conditions in the speech recognition system.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation-in-part of co-pending U.S.application Ser. No. 09/177,461, entitled “Method For Reducing NoiseDistortions In A Speech Recognition System,” filed Oct. 22, 1998. Thisapplication is also related to, and claims the benefit of, U.S.Provisional Application No. 60/121,678, entitled “Adaptive Non-LinearNoise Attenuation For Speech Recognition And Speech EnhancementApplications,” filed Feb. 25, 1999. These related applications arecommonly assigned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to electronic speech recognitionsystems and relates more particularly to an apparatus and method fornoise attenuation in a speech recognition system.

2. Description of the Background Art

Implementing an effective and efficient method for system users tointerface with electronic devices is a significant consideration ofsystem designers and manufacturers. Automatic speech recognition is onepromising technique that allows a system user to effectively communicatewith selected electronic devices, such as digital computer systems.Speech typically consists of one or more spoken utterances which eachmay include a single word or a series of closely-spaced words forming aphrase or a sentence.

Conditions with significant ambient background noise levels presentadditional difficulties when implementing a speech recognition system.Examples of such noisy conditions may include speech recognition inautomobiles or in certain manufacturing facilities. To accuratelyanalyze a particular utterance in such user applications, a speechrecognition system may be required to selectively differentiate betweena spoken utterance and the ambient background noise.

Referring now to FIG. 1(a), an exemplary waveform diagram for oneembodiment of noisy speech 112 is shown. In addition, FIG. 1(b) depictsan exemplary waveform diagram for one embodiment of speech 114 withoutnoise. Similarly, FIG. 1(c) shows an exemplary waveform diagram for oneembodiment of noise 116 without speech 114. In practice, noisy speech112 of FIG. 1(a) therefore is typically comprised of several components,including speech 114 of FIG. (1(b) and noise 116 of FIG. 1(c). In FIGS.1(a), 1(b), and 1(c), waveforms 112, 114, and 116 are presented forpurposes of illustration only. The present invention may readilyincorporate various other embodiments of noisy speech 112, speech 114,and noise 116.

The two main sources that typically create acoustic distortion are thepresence of additive noise (such as car noise, music or backgroundspeakers), and convolutive distortions due to the use of variousdifferent microphones, use of a telephone channel, or reverberationeffects. Different types of additive noise will have different signalcharacteristics. A speech recognition system designed to reduce one typeof additive noise may not be robust to other types of additive noise,thereby reducing the effectiveness of the system.

From the foregoing discussion, it therefore becomes apparent that noiseattenuation in a speech recognition system is a significantconsideration of system designers and manufacturers of speechrecognition systems.

SUMMARY OF THE INVENTION

In accordance with the present invention, an apparatus and method aredisclosed for noise attenuation in a speech recognition system. Theinvention includes a noise suppressor configured to attenuate noise in anoisy speech signal, and a processor coupled to the system to controlthe noise suppressor. The noise suppressor utilizes statisticalcharacteristics of the noise signal to attenuate amplitude values of thenoisy speech signal that have a probability of containing noise.

In one embodiment, a Fast Fourier transformer generates amplitude energyvalues for the noisy speech signal in units of frames. The Fast Fouriertransformer also generates amplitude energy values for a noise signal inunits of frames. The amplitude energy values may be magnitude energyvalues or power energy values.

The noise suppressor preferably utilizes an attenuation function havinga shape determined in part by a noise average and a noise standarddeviation. The shape of the attenuation function as the functionincreases is an inverse of the shape of a probability density curve of anoise signal. The noise average determines where the attenuationfunction begins to increase from a maximum attenuation level, which isdetermined by an attenuation coefficient. The noise standard deviationdetermines the shape of the attenuation function as the functionincreases from the maximum attenuation level to unity, or fulltransmission.

In a further embodiment, the noise suppressor also utilizes an adaptiveattenuation coefficient that depends on signal-to-noise conditions inthe speech recognition system. The adaptive attenuation coefficient willtypically be larger for high noise conditions, and smaller for low noiseconditions. The adaptive attenuation coefficient also depends onfrequency because noise typically does not affect the speech signalequally at all frequencies.

The noise suppressor of the present invention provides attenuated noisyspeech energy to a filter bank. The filter bank filters the attenuatednoisy speech energy into channel energy, and then provides the channelenergy to a logarithmic compressor to be converted to logarithmicchannel energy. A frequency cosine transformer then converts thelogarithmic channel energy into corresponding static features that areseparately provided to a normalizer, a first time cosine transformer,and a second time cosine transformer.

The first time cosine transformer converts the static features intodelta features that are provided to the normalizer. Similarly, thesecond time cosine transformer converts the static features intodelta-delta features that are also provided to the normalizer. Thenormalizer performs a normalization procedure on the static features togenerate normalized static features to a recognizer. The normalizer alsoperforms a normalization procedure on the delta features and delta-deltafeatures to generate normalized delta features and normalizeddelta-delta features, respectively, to the recognizer.

The recognizer analyzes the normalized static features, the normalizeddelta features, and the normalized delta-delta features to generate aspeech recognition result, according to the present invention. Thepresent invention thus efficiently and effectively implements anapparatus and method for noise attenuation in a speech recognitionsystem.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1(a) is an exemplary waveform diagram for one embodiment of noisyspeech;

FIG. 1(b) is an exemplary waveform diagram for one embodiment of speechwithout noise;

FIG. 1(c) is an exemplary waveform diagram for one embodiment of noisewithout speech;

FIG. 2 is a block diagram for one embodiment of a computer system,according to the present invention;

FIG. 3 is a block diagram for one embodiment of the memory of FIG. 2,according to the present invention;

FIG. 4 is a block diagram for one embodiment of the speech module ofFIG. 3, according to the present invention;

FIG. 5 is an exemplary waveform diagram for one embodiment of frames ofnoise and noisy speech, according to the present invention;

FIG. 6 is a block diagram for one embodiment of the feature extractor ofFIG. 4, according to the present invention;

FIG. 7 is a schematic diagram for one embodiment of the filter bank ofFIG. 6, according to the present invention;

FIG. 8(a) is a diagram of a probability density of noise energy and aprobability density of speech energy, according to one embodiment of thepresent invention;

FIG. 8(b) is a diagram of a probability density of noisy speech energy,according to one embodiment of the present invention;

FIG. 9(a) is a diagram of an attenuation function, according to oneembodiment of the present invention;

FIG. 9(b) is a diagram of a probability density of noise energy and anattenuation function, according to one embodiment of the presentinvention; and

FIG. 10 is a flowchart of method steps for noise attenuation, accordingto one embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention relates to an improvement in speech recognitionsystems. The following description is presented to enable one ofordinary skill in the art to make and use the invention and is providedin the context of a patent application and its requirements. Variousmodifications to the preferred embodiment will be readily apparent tothose skilled in the art and the generic principles herein may beapplied to other embodiments. Thus, the present invention is notintended to be limited to the embodiment shown, but is to be accordedthe widest scope consistent with the principles and features describedherein.

The present invention includes a noise suppressor configured toattenuate noise in a noisy speech signal in an electronic system, and aprocessor coupled to the system to control the noise suppressor. Thenoise suppressor utilizes statistical characteristics of a noise signalto attenuate amplitude values of the noisy speech signal that have aprobability of containing noise. In one embodiment, the noise suppressorutilizes an attenuation function having a shape determined in part by anoise average and a noise standard deviation. In a further embodiment,the noise suppressor also utilizes an adaptive attenuation coefficientthat depends on signal-to-noise conditions in the speech recognitionsystem.

Referring now to FIG. 2, a block diagram for one embodiment of acomputer system 210 is shown, according to the present invention. TheFIG. 2 embodiment includes a sound sensor 212, an amplifier 216, ananalog-to-digital converter 220, a central processing unit (CPU) 228, amemory 230 and an input/output interface 232.

In operation, sound sensor 212 detects ambient sounds and converts thedetected sounds into an analog sound signal that is provided toamplifier 216 via line 214. Amplifier 216 amplifies the received analogsound signal and provides an amplified analog sound signal toanalog-to-digital converter 220 via line 218. Analog-to-digitalconverter 220 then converts the amplified analog sound signal intocorresponding digital sound data and provides the digital sound data vialine 222 to system bus 224.

CPU 228 may then access the digital sound data on system bus 224 andresponsively analyze and process the digital sound data to performspeech recognition according to software instructions contained inmemory 230. The operation of CPU 228 and the software instructions inmemory 230 are further discussed below in conjunction with FIGS. 3-10.After the sound data is processed, CPU 228 may then advantageouslyprovide the results of the speech recognition analysis to other devices(not shown) via input/output interface 232.

Referring now to FIG. 3, a block diagram for one embodiment of memory230 of FIG. 2 is shown. Memory 230 may alternatively comprise variousstorage-device configurations, including Random-Access Memory (RAM) andnon-volatile storage devices such as floppy disks or hard disk drives.In the FIG. 3 embodiment, memory 230 includes a speech module 310, aspeech average register 312, a noise average register 314, a noisesecond moment register 316, a noise standard deviation register 318, andan adaptive attenuation register 320. Memory 230 may also includevarious other registers and software modules.

In the FIG. 3 embodiment, speech module 310 includes a series ofsoftware modules which are executed by CPU 228 to analyze and detectspeech data, and which are further described below in conjunction withFIGS. 4 through 10. In alternate embodiments, speech module 310 mayreadily be implemented using various other software and/or hardwareconfigurations. Speech average register 312, noise average register 314,noise second moment register 316, noise standard deviation register 318,and adaptive attenuation register 320 contain respective variable valuesthat are calculated and utilized by speech module 310 to attenuate noiseaccording to the present invention. The utilization and functionality ofspeech average register 312, noise average register 314, noise secondmoment register 316, noise standard deviation register 318, and adaptiveattenuation register 320 are related to a noise suppressor, as describedbelow in conjunction with FIGS. 6 through 10.

Referring now to FIG. 4, a block diagram for one embodiment of the FIG.3 speech module 310 is shown, according to the present invention. In theFIG. 3 embodiment, speech module 310 includes a feature extractor 410,an endpoint detector 414 and a recognizer 418.

In operation, analog-to-digital converter 220 (FIG. 2) provides digitalsound data to feature extractor 410 within speech module 310 via systembus 224. Feature extractor 410 responsively generates normalized featurevectors that are then provided to recognizer 418 via path 416. Endpointdetector 414 analyzes sound data received from feature extractor 410,and responsively determines endpoints (beginning and ending points) forspoken utterances represented by the sound data received via path 428.Endpoint detector 414 then provides the calculated endpoints to featureextractor 410 via path 430 and to recognizer 418 via path 432.

Recognizer 418 receives the normalized feature vectors via path 416 andthe endpoints via path 432, and responsively performs a speechrecognition procedure to advantageously generate a speech recognitionresult to CPU 228 via path 424. In the FIG. 4 embodiment, recognizer 418may effectively be implemented as a Hidden Markov Model (HMM)recognizer.

Referring now to FIG. 5, a diagram for one embodiment of frames of noiseand noisy speech is shown, according to the present invention. Sounddetected by sound sensor 212 (FIG. 2) will typically include periods ofnoise and periods of noisy speech. In FIG. 5, the detected soundincludes noise 542, noisy speech 544, noise 546, and noisy speech 548.The detected waveform in FIG. 5 is shown for purposes of illustrationonly, and sound detected by the present invention may comprise variousother waveforms.

Speech module 310 processes sound data in units called frames. A frame530 contains sound data for a predetermined amount of time, typically anumber of milliseconds. In FIG. 5, noise 542 includes four frames andnoisy speech 544 includes five frames. The five frames of noisy speech544 correspond to an utterance 512. Utterance 512 has an endpoint 522and an endpoint 524, which are detected by endpoint detector 414. Anutterance 516 includes four frames and has endpoints 526 and 528. Thefour frames of noise 542 correspond to a noise period 510, and the threeframes of noise 546 correspond to a noise period 514. Other utterancesand noise periods may contain different numbers of frames from thoseshown in FIG. 5.

Referring now to FIG. 6, a block diagram for one embodiment of the FIG.4 feature extractor 410 is shown, according to the present invention. Inthe FIG. 6 embodiment, feature extractor 410 includes a Fast FourierTransformer 614, a noise suppressor 618, a filter bank 622, alogarithmic compressor 626, a frequency cosine transformer 630, a firsttime cosine transformer 636, a second time cosine transformer 640, and anormalizer 646. In alternate embodiments, feature extractor 410 mayreadily be implemented using various other appropriate configurations.

In operation, the FIG. 6 feature extractor 410 initially provides sourcesound data to Fast Fourier Transformer (FFT) 614 via path 224. FFT 614responsively generates frequency-domain sound data by converting thesource sound data from the time domain to the frequency domain tofacilitate subsequent noise suppression. Fast Fourier transforms arediscussed in “Digital Signal Processing Principles, Algorithms andApplications,” by John G. Proakis and Dimitris G. Manolakis, 1992,Macmillan Publishing Company, (in particular, pages 706-708) which ishereby incorporated by reference.

FFT 614 processes sound data on a frame by frame basis, generatingamplitude energy values for each frame of data. In the FIG. 6embodiment, FFT 614 produces an amplitude energy value for each of 256frequency indexes. The amplitude energy values may be magnitude energyvalues or power energy values. FFT 614 then preferably provides thegenerated amplitude energy values to noise suppressor 618 via path 616.

In the FIG. 6 embodiment, noise suppressor 618 preferably performs anoise suppression process for each frame of sound data. Noise suppressor618 provides the noise-suppressed sound energy to filter bank 622 viapath 620. The functionality of noise suppressor 618 is further discussedbelow in conjunction with FIGS. 8-10.

Filter bank 622 responsively filters the noise-suppressed sound energyinto channel energy by dividing the noise-suppressed sound energy into anumber of frequency sub-bands. The configuration and functionality offilter bank 622 is further discussed below in conjunction with FIG. 7.Filter bank 622 then provides the filtered channel energy to logarithmiccompressor 626 via path 624. Logarithmic compressor 626 then preferablyconverts the filtered channel energy received from filter bank 622 intologarithmic channel energy by separately calculating the logarithm ofeach frequency sub-band that comprises the filtered channel energy.Logarithmic compressor 626 then provides the logarithmic channel energyto frequency cosine transformer 630 via path 628.

In the FIG. 6 embodiment, frequency cosine transformer 630 performs alinear transformation process that decorrelates the logarithmic channelenergy received from logarithmic compressor 626. Adjacent channels offilter bank 622 may exhibit similar responses that result indisadvantageous correlations between sub-band energy values. Frequencycosine transform 630 preferably converts the channels (sub-bands) ofreceived logarithmic channel energy into independent cepstral featuresthat are compatible with an HMM recognizer such as the preferredembodiment of recognizer 418. The cepstral features preferably include anumber of separate feature components.

The foregoing frequency cosine transform process and correspondingderivation of cepstral features are further discussed in the followingreferences which are hereby incorporated by reference: “SpeechCommunication,” by Douglas O'Shaughnessy, 1990, Addison-WesleyPublishing, (in particular, pages 422-423), and “Comparison OfParametric Representations For Monosyllabic Word Recognition InContinuously Spoken Sentences,” by S. B. Davis and Paul Mermelstein,1980, IEEE.

Frequency cosine transformer 630 thus converts the received logarithmicchannel energy into corresponding static features that are provided tonormalizer 646 via path 632. Frequency cosine transformer 630 alsoprovides the static features to first time cosine transformer 636 viapath 634, and to second time cosine transformer 640 via path 638. Inalternate embodiments of feature extractor 410, additional time cosinetransforms may readily be utilized. For example, frequency cosinetransformer 630 may provide the static features to additional timecosine transformers, in accordance with the present invention.

First time cosine transformer 636 responsively converts the receivedstatic features into delta features that are provided to normalizer 646via path 642. Similarly, second time cosine transformer 640 converts thereceived static features into delta-delta features that are provided tonormalizer 646 via path 644.

First time cosine transformer 636 and second time cosine transformer 640remove the continuous component of the static cepstral features fromfrequency cosine transformer 630 to provide linear channel andmicrophone invariance to the generated delta features and delta-deltafeatures. In a phoneme-based recognizer (like the preferred embodimentof recognizer 418) elimination of the static features may significantlydegrade speech recognition accuracy. In accordance with the presentinvention, the time-domain cosine transform is therefore used toestimate derivative features (1st, 2nd and in some cases 3rdderivatives) in combination with the static features.

Use of first time cosine transformer 636 and second time cosinetransformer 640 in adverse conditions provides more stable derivativesin mismatched conditions (unknown channels and additive noise). Thetime-domain cosine transform estimates derivatives on an orthogonalbasis to provide more separability and stability in adverse conditions.

In one embodiment, the process performed by first time cosinetransformer 636 and second time cosine transformer 640 may be expressedby the following formula:${\frac{{\partial\,^{o}}\quad}{{\partial\,_{t}}\quad}\quad C_{t}\quad (p)} = {\sum\limits_{i = {- M}}^{M}\quad {C_{t + k}\quad (p)\quad \cos \quad \left( {\frac{i + M + 0.5}{{2M} + 1}\quad o\quad \pi} \right)}}$

where C_(t)(p) is the p^(th) cepstral coefficient at time frame t, o isthe derivatives order (1st, 2nd derivatives . . . ) with a value of onecorresponding to the delta features and a value of two corresponding tothe delta-delta features, and M is half of a window analysis used toestimate the differential coefficients.

Finally, normalizer 646 performs an effective normalization process onthe received static features to generate normalized static features torecognizer 418 via path 416(a), in accordance with the presentinvention. Similarly, normalizer 646 performs a normalization process onthe received delta features to generate normalized delta features torecognizer 418 via path 416(b). Normalizer 646 also performs anormalization process on the received delta-delta features to generatenormalized delta-delta features to recognizer 418 via path 416(c).

Referring now to FIG. 7, a schematic diagram for one embodiment offilter bank 622 of feature extractor 410 (FIG. 4) is shown, according tothe present invention. In the FIG. 7 embodiment, filter bank 622 is amel-frequency scaled filter bank with “p” channels (channel 0 (714)through channel p (722)). In alternate embodiments, various otherimplementations of filter bank 622 are equally possible.

In operation, filter bank 622 receives noise-suppressed sound energy viapath 620, and provides the noise-suppressed sound energy in parallel tochannel 0 (714) through channel p (722). In response, channel 0 (714)through channel p (722) generate respective channel energies E_(o)through E_(p) which collectively form the filtered channel energyprovided to logarithmic compressor 626 via path 624.

Referring now to FIG. 8(a), a diagram of an exemplary probabilitydensity of noise energy 812 and an exemplary probability density ofspeech energy 814 is shown, according to one embodiment of the presentinvention. A probability density typically represents the likelihoodthat a random signal, such as noise, will have a certain amplitudeenergy value. As shown in FIG. 8(a), noise density 812 is typicallyconcentrated at low amplitude energy values and speech density 814 istypically concentrated at high amplitude energy values.

Noise density 812 is approximately Gaussian with a maximum value P atamplitude energy μ. The value μ is an average of the noise amplitudevalues, or noise average. A noise standard deviation σ is an indicatorof the spread of noise density 812 about the noise average. The width ofnoise density 812 at a value 0.607 times the maximum value P is equal totwo times the noise standard deviation (2σ). Additive noise fromdifferent sources will have different probability densities, each with adifferent noise average and noise standard deviation.

Referring now to FIG. 8(b), a diagram of an exemplary probabilitydensity of noisy speech energy 820 is shown, according to one embodimentof the present invention. Noisy speech density 820 occurs in situationswhere additive noise corrupts a speech signal. Additive noise typicallyaffects noisy speech density 820 at low amplitude energy values. Noisesuppressor 618 (FIG. 6) advantageously attenuates noisy speech density820 such that noise is suppressed in the sound energy transmitted tofilter bank 622, as described below in conjunction with FIGS. 9-11.

Referring now to FIG. 9(a), a diagram of an attenuation function 912 isshown, according to one embodiment of the present invention. Inaccordance with the present invention, noise suppressor 618 preferablyreduces noise in sound energy by multiplying noisy speech energy havingdensity 820 by attenuation function 912. The shape of attenuationfunction 912 depends in part on the noise average and the noise standarddeviation. The noise average determines where attenuation function 912begins to increase from the maximum attenuation (max atten) level. Thenoise standard deviation determines the shape of attenuation function912 as the amplitude changes from the maximum attenuation level to unity(minimum attenuation or full transmission).

In one embodiment of the present invention, noise suppressor 618preferably generates attenuated noisy speech energy as follows:$\begin{matrix}{{Yat}_{k} = \frac{Y_{k}}{1 + A_{e}^{{- \frac{1}{2}}\quad {(\frac{Y_{k} - {\alpha \quad \mu_{k}}}{\sigma_{k}})}^{2}}}} & {{{if}\quad Y_{k}} > {\alpha \quad \mu_{k}}} \\{{Yat}_{k} = \frac{Y_{k}}{1 + A}} & {otherwise}\end{matrix}$

where Yat_(k) is the attenuated noisy speech energy at frequency indexk, Y_(k) is noisy speech energy at frequency index k, μ_(k) is the noiseaverage at frequency index k, σ_(k) is the noise standard deviation atfrequency index k, α is an overestimation coefficient, and A is anattenuation coefficient. Optimum values for α and A may be determinedexperimentally. In the FIG. 9(a) embodiment, α is equal to 1.3 and A isequal to 6. Noise suppressor 618 preferably generates attenuated noisyspeech energy at 256 frequency indexes for each frame of noisy speechenergy.

In another embodiment of the present invention, noise suppressor 618preferably generates the attenuated noisy speech energy as follows:$\begin{matrix}{{Yat}_{k} = \frac{Y_{k}}{1 + A_{}^{{- \frac{1}{2}}\quad {(\frac{Y_{k} - {({\mu_{k} + {\alpha_{v}\quad \sigma_{k}}})}}{\sigma_{k}})}^{2}}}} & {{{if}\quad Y_{k}} > {\mu_{k} + {\alpha_{v}\quad \sigma_{k}}}} \\{{Yat}_{k} = \frac{Y_{k}}{1 + A}} & {otherwise}\end{matrix}$

where Yat_(k) is the attenuated noisy speech energy at frequency indexk, Y_(k) is the noisy speech energy at frequency index k, μ_(k) is thenoise average at frequency index k, σ_(k) is the noise standarddeviation at frequency index k, α_(v) is an overestimation coefficientrelated to the noise standard deviation, and A is an attenuationcoefficient. Optimum values for α_(v) and A may be determinedexperimentally. In the FIG. 9(a) embodiment, α_(v) is equal to 0.75 andA is equal to 6. Noise suppressor 618 generates attenuated noisy speechenergy at 256 frequency indexes for each frame of noisy speech energy.

In FIG. 9(a), the overestimation coefficient times the noise average(αμ) is the amplitude energy value where attenuation function 912 beginsto increase from the maximum attenuation value. Other noise densitieshaving the same noise average but different noise standard deviationsmay result in differently shaped attenuation functions such as functions914 and 916.

Referring now to FIG. 9(b), a diagram of a probability density 932 ofnoise energy and an attenuation function 918 is shown, according to oneembodiment of the present invention. Attenuation function 918 preferablydepends on the noise average and the noise standard deviation of noisedensity 932. The shape of attenuation function 918 as the functionincreases from maximum attenuation is preferably an inverse of the shape934 of noise density 932 as noise density 932 decreases from a maximumvalue.

Before generating the attenuated noisy speech energy, noise suppressor618 preferably determines the noise average and the noise standarddeviation for each frequency index k. In one embodiment, noisesuppressor 618 may determine the noise average during noise periods 510(FIG. 5) as follows:$\mu_{k} = {\frac{1}{T}\quad {\sum\limits_{t = 1}^{T}\quad {N_{k}\quad (t)}}}$

where μ_(k) is the noise average for frequency index k, N_(k)(t) isnoise energy for frequency index k at frame t for t equal to 1 throughT, and T is the total number of frames in the noise period. Endpointdetector 414 (FIG. 4) provides endpoint data to noise suppressor 618 toindicate whether a frame is in a noise period or an utterance. Noisesuppressor 618 preferably stores the noise average in noise averageregister 314 (FIG. 3).

Noise suppressor 618 may then determine the noise standard deviation asfollows:$\sigma_{k} = \sqrt{\frac{1}{T}\quad {\sum\limits_{t = 1}^{T}\quad \left( {{N_{k}\quad (t)} - \mu_{k}} \right)^{2}}}$

where σ_(k) is the noise standard deviation for frequency index k, μ_(k)is the noise average for frequency index k, N_(k)(t) is the noise energyfor frequency index k at frame t for t equal to 1 through T, and T isthe total number of frames in the noise period. Noise suppressor 618preferably stores the noise standard deviation in noise standarddeviation register 318.

In another embodiment, noise suppressor 618 determines the noise averageand the noise standard deviation recursively at each frame t. In thisembodiment, noise suppressor 618 determines the noise average asfollows:

 μ_(k)(t)=βμ_(k)(t−1)+(1−β)N _(k)(t)

where μ_(k)(t) is the noise average for frequency index k at frame t,N_(k)(t) is the noise energy for frequency index k at frame t, and β isa noise forgetting coefficient. The noise forgetting coefficient istypically equal to 0.95.

To determine the noise standard deviation recursively, noise suppressor618 first determines a noise second moment as follows:

S _(k)(t)=βS _(k)(t−1)+(1−β)N _(k)(t)N _(k)(t)

where S_(k)(t) is the noise second moment for frequency index k at framet, N_(k)(t) is the noise energy for frequency index k at frame t, and βis the noise forgetting coefficient. Noise suppressor 618 preferablystores the noise second moment in noise second moment register 316 (FIG.3).

Noise suppressor 618 then determines the noise standard deviation asfollows:

σ_(k)(t)={square root over (S _(k)(t)−μ_(k)(t)μ_(k)(t))}

where σ_(k)(t) is the noise standard deviation for frequency index k atframe t, S_(k)(t) is the noise second moment for frequency index k atframe t, and μ_(k)(t) is the noise average for frequency index k atframe t. Noise suppressor 618 preferably stores the noise standarddeviation values in noise standard deviation register 318. Noisesuppressor 618 then utilizes the noise average and the noise standarddeviation to generate attenuated noisy speech energy as described above.

In a further embodiment of the present invention, the attenuationcoefficient A may depend on the signal-to-noise conditions instead ofbeing a constant. A large attenuation coefficient provides betterattenuation in high noise conditions and a small attenuation coefficientprovides better attenuation in low noise conditions. In addition, noiseenergy typically does not affect the speech energy equally at allfrequencies. Thus, noise suppressor 618 may determine an adaptiveattenuation coefficient for each frequency index k at each frame asfollows:${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad (t)}{\alpha \quad \mu_{k}\quad ({prev})}} \right)}\quad t} \in {utterance}}$${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad ({prev})}{\alpha \quad \mu_{k}\quad (t)}} \right)}\quad t} \in {{noise}\quad {period}}}$

where A_(k)(t) is the adaptive attenuation coefficient for frequencyindex k at frame t, A is the attenuation coefficient, μ_(k)(t) is thenoise average for frequency index k at frame t, α is the overestimationcoefficient, Sp_(k)(t) is a noisy speech average for frequency index kat frame t, μ_(k)(prev) is a noise average for a noise periodimmediately previous to a current utterance, and Sp_(k)(prev) is a noisyspeech average for an utterance immediately previous to a current noiseperiod. Noise suppressor 618 preferably stores the adaptive attenuationcoefficients in adaptive attenuation register 320 (FIG. 3).

Noise suppressor 618 determines the noise average for each frame in anoise period as described above. Noise suppressor 618 determines thenoisy speech average for each frame in an utterance as follows:

Sp _(k)(t)=ySp _(k)(t−1)+(1−y)Y _(k)(t)

where Sp_(k)(t) is the noisy speech average for frequency index k atframe t, Y_(k)(t) is a noisy speech energy value for frequency index kat frame t, and y is a speech forgetting coefficient. The speechforgetting coefficient typically has a value close to 1, for instance0.995 or 0.997. Noise suppressor 618 preferably stores the noisy speechaverage values in speech average register 312 (FIG. 3).

Referring now to FIG. 10, a flowchart of method steps for noiseattenuation of a frame of sound data is shown, according to oneembodiment of the present invention. First, in step 1012, FFT 612generates amplitude energy values for the frame of sound data. Next, instep 1014, noise suppressor 618 evaluates whether the amplitude energyvalues for the frame are speech energy or noise energy. Noise suppressor618 may receive endpoint data from endpoint detector 414 to indicate thebeginning and ending of an utterance.

If the amplitude energy values are speech energy, then in step 1022,noise suppressor 618 calculates a noisy speech average as describedabove in conjunction with FIG. 9(b). The FIG. 10 method then continueswith step 1024.

However, if the amplitude energy values are noise energy, then, in step1016, noise suppressor 618 calculates a noise average as described abovein conjunction with FIG. 9(b). Next, in step 1018, noise suppressor 618calculates a noise second moment as described above in conjunction withFIG. 9(b). In step 1020, noise suppressor 618 uses the noise average andnoise second moment to calculate a noise standard deviation, asdescribed above in conjunction with FIG. 9(b).

In step 1024, noise suppressor 618 calculates an adaptive attenuationcoefficient for every frequency k for the frame of sound energy, asdescribed above in conjunction with FIG. 9(b). Then, in step 1026, noisesuppressor 618 generates attenuated noisy speech energy for the frame asdescribed above in conjunction with FIG. 9(a). Noise suppressor 618 thenprovides the attenuated noisy speech energy to filter bank 622 forfurther processing as described above in conjunction with FIG. 6. Themethod steps described above are performed for consecutive frames ofdetected sound data. Thus the present invention effectively attenuatesnoise in a speech recognition system.

The invention has been explained above with reference to a preferredembodiment. Other embodiments will be apparent to those skilled in theart in light of this disclosure. For example, the present invention mayreadily be implemented using configurations and techniques other thanthose described in the preferred embodiment above. Additionally, thepresent invention may effectively be used in conjunction with systemsother than the one described above as the preferred embodiment.Therefore, these and other variations upon the preferred embodiments areintended to be covered by the present invention, which is limited onlyby the appended claims.

What is claimed is:
 1. An apparatus for noise attenuation in anelectronic system, comprising: a noise suppressor configured toselectively attenuate additive noise in an electronic signal, saidelectronic signal being a noisy speech signal that includes a noisesignal combined with a speech signal, said noise suppressor selectivelyattenuating said noise signal by utilizing statistical characteristicsof amplitude energy values of said noise signal, said statisticalcharacteristics of said amplitude energy values of said noise signalinclude a noise average and a noise standard deviation, said noisesuppressor generating an attenuated noisy speech signal according to aformula: $\begin{matrix}{{Yat}_{k} = \frac{Y_{k}}{1 + A_{e}^{{- \frac{1}{2}}\quad {(\frac{Y_{k} - {\alpha \quad \mu_{k}}}{\sigma_{k}})}^{2}}}} & {{{if}\quad Y_{k}} > {\alpha \quad \mu_{k}}} \\{{Yat}_{k} = \frac{Y_{k}}{1 + A}} & {otherwise}\end{matrix}$

 where Yat_(k) is said attenuated noisy speech signal for a frequency k,Y_(k) is said noisy speech signal for said frequency k, μ_(k) is saidnoise average for said frequency k, σ_(k) is said noise standarddeviation for said frequency k, α is a overestimation coefficient, and Ais an attenuation coefficient; and a processor coupled to saidelectronic system to control said noise suppressor.
 2. The apparatus ofclaim 1, wherein said electronic includes a speech recognition system.3. The apparatus of claim 2, wherein said speech recognition system isimplemented in a motor vehicle.
 4. The apparatus of claim 1, whereinsaid noise suppressor selectively attenuates said noise signal using anattenuation function that varies from a maximum attenuation to a minimumattenuation in a manner inverse to a probability density curve of saidnoise signal.
 5. The apparatus of claim 1, wherein said attenuationcoefficient includes an adaptive attenuation coefficient that isdependent on a frequency and a signal-to-noise ratio of said noisyspeech signal.
 6. The apparatus of claim 1, wherein said attenuationcoefficient is replaced by an adaptive attenuation coefficientdetermined according to a formula:${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad (t)}{\alpha \quad \mu_{k}\quad ({prev})}} \right)}\quad t} \in {utterance}}$${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad ({prev})}{\alpha \quad \mu_{k}\quad (t)}} \right)}\quad t} \in {{noise}\quad {period}}}$

where A_(k)(t) is said adaptive attenuation coefficient for a frequencyindex k at a frame t, A is said attenuation coefficient, α is saidoverestimation coefficient, μ_(k)(t) is said noise average for frequencyindex k at frame t, Sp_(k)(t) is a noisy speech average for frequencyindex k at frame t, μ_(k)(prev) is a noise average for a noise periodimmediately previous to a current utterance, and Sp_(k)(prev) is a noisyspeech average for an utterance immediately previous to a current noiseperiod.
 7. The apparatus of claim 6, wherein said noise suppressorcalculates said noisy speech average according to a formula: Sp_(k)(t)=ySp _(k)(t−1)+(1−y)Y _(k)(t) where Sp_(k)(t) is said noisyspeech average for frequency index k at frame t, Y_(k)(t) is a noisyspeech amplitude energy value for frequency index k at frame t, and y isa speech forgetting coefficient.
 8. The apparatus of claim 1, whereinsaid noise suppressor determines a noise average and a noise standarddeviation of said energy amplitude values of said noise signal, utilizessaid noise average and said noise standard deviation to identifyselected ones of said amplitude energy values of said noisy speechsignal that have a probability of containing noise, and selectivelyattenuates said amplitude energy values of said noisy speech signalaccording to said probability.
 9. The apparatus of claim 1, wherein saidnoise suppressor calculates said noise average according to a formula:$\mu_{k} = {\frac{1}{T}\quad {\sum\limits_{t = 1}^{T}\quad {N_{k}\quad (t)}}}$

where μ_(k) is said noise average for a frequency index k, N_(k)(t) is anoise energy amplitude value for frequency index k at a frame t for tequal to 1 through T, and T is a total number of frames in a noiseperiod.
 10. The apparatus of claim 9, wherein said noise suppressorcalculates said noise standard deviation according to a formula:$\sigma_{k} = \sqrt{\frac{1}{T}\quad {\sum\limits_{t = 1}^{T}\quad \left( {{N_{k}\quad (t)} - \mu_{k}} \right)^{2}}}$

where σ_(k) is said noise standard deviation for frequency index k,μ_(k) is said noise average for frequency index k, N_(k)(t) is saidnoise energy amplitude value for frequency index k at said frame t for tequal to 1 through T, and T is said total number of frames in said noiseperiod.
 11. An apparatus for noise attenuation in an electronic system,comprising: a noise suppressor configured to selectively attenuateadditive noise in an electronic signal, said electronic signal being anoisy speech signal that includes a noise signal combined with a speechsignal, said noise suppressor selective attenuating said noise signal byutilizing statistical characteristics of amplitude energy values of saidnoise signal, said statistical characteristics of said amplitude energyvalues of said noise signal include a noise average and a noise standarddeviation, said noise suppressor generating an attenuated noisy speechsignal according to a formula:${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad (t)}{\alpha \quad \mu_{k}\quad ({prev})}} \right)}\quad t} \in {utterance}}$${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad ({prev})}{\alpha \quad \mu_{k}\quad (t)}} \right)}\quad t} \in {{noise}\quad {period}}}$

 where Yat_(k) is said attenuated noisy speech signal for a frequency k,Y_(k) is said noisy speech signal for said frequency k, μ_(k) is saidnoise average for said frequency k, σ_(k) is said noise standarddeviation for said frequency k, α_(v) is an overestimation coefficientrelated to said noise standard deviation, and A is an attenuationcoefficient; and a processor coupled to said electronic system tocontrol said noise suppressor.
 12. An apparatus for noise attenuation inan electronic system, comprising: a noise suppressor configured toselectively attenuate additive noise in an electronic signal, saidelectronic signal being a noisy speech signal that includes a noisesignal combined with a speech signal, said noise suppressor selectivelyattenuating said noise signal by utilizing statistical characteristicsof amplitude energy values of said noise signal, said statisticalcharacteristics of said amplitude energy values of said noise signalinclude a noise average and a noise standard deviation, said noisesuppressor calculating said noise average according to a formula:μ_(k)(t)=βμ_(k)(t−1)+(1−β)N _(k)(t)  where μ_(k)(t) is said noiseaverage for a frequency index k at a frame t, N_(k)(t) is a noise energyamplitude value for frequency index k at frame t, and β is a noiseforgetting coefficient; and a processor coupled to said electronicsystem to control said noise suppressor.
 13. The apparatus of claim 12,wherein said noise suppressor calculates a noise second moment accordingto a formula: S _(k)(t)=βS _(k)(t−1)+(1−β)N _(k)(t)N _(k)(t) whereS_(k)(t) is said noise second moment for frequency index k at frame t,N_(k)(t) is said noise energy amplitude value for frequency index k atframe t, and β is said noise forgetting coefficient.
 14. The apparatusof claim 13, wherein said noise suppressor calculates said noisestandard deviation according to a formula: σ_(k)(t)={square root over (S_(k)(t)−μ_(k)(t)μ_(k)(t))} where σ_(k)(t) is said noise standarddeviation for frequency index k at frame t, S_(k)(t) is said noisesecond moment for frequency index k at frame t, and μ_(k)(t) is saidnoise average for frequency index k at frame t.
 15. A method for noiseattenuation in an electronic system, comprising the steps of:selectively attenuating additive noise in an electronic signal using anoise suppressor, said electronic signal being a noisy speech signalthat includes a noise signal combined with a speech signal, said noisesuppressor selectively attenuating said noise signal by utilizingstatistical characteristics of amplitude energy values of said noisesignal, said statistical characteristics of said amplitude energy valuesof said noise signal include a noise average and a noise standarddeviation, said noise suppressor generating an attenuated noisy speechsignal according to a formula: $\begin{matrix}{{Yat}_{k} = \frac{Y_{k}}{1 + A_{e}^{{- \frac{1}{2}}\quad {(\frac{Y_{k} - {\alpha \quad \mu_{k}}}{\sigma_{k}})}^{2}}}} & {{{if}\quad Y_{k}} > {\alpha \quad \mu_{k}}} \\{{Yat}_{k} = \frac{Y_{k}}{1 + A}} & {otherwise}\end{matrix}$

 where Yat_(k) said attenuated noisy speech for signal for a frequencyk, Y_(k) is said noisy speech signal for said frequency k, μ_(k) is saidnoise average for said frequency k, σ_(k) is said noise standarddeviation for said frequency k, α is a overestimation coefficient, and Ais an attenuation coefficient; and controlling said noise suppressorwith a processor coupled to said electronic system.
 16. The method ofclaim 15, wherein said electronic includes a speech recognition system.17. The method of claim 16, wherein said speech recognition system isimplemented in a motor vehicle.
 18. The method of claim 15, wherein saidnoise suppressor selectively attenuates said noise signal using anattenuation function that varies from a maximum attenuation to a minimumattenuation in a manner inverse to a probability density curve of saidnoise signal.
 19. The method of claim 15, wherein said attenuationcoefficient includes an adaptive attenuation coefficient that isdependent on a frequency and a signal-to-noise ratio of said noisyspeech signal.
 20. The method of claim 15, wherein said attenuationcoefficient is replaced by an adaptive attenuation coefficientdetermined according to a formula:${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad (t)}{\alpha \quad \mu_{k}\quad ({prev})}} \right)}\quad t} \in {utterance}}$${A_{k}\quad (t)} = {{\frac{A}{\log_{2}\quad \left( {1 + \frac{{Sp}_{k}\quad ({prev})}{\alpha \quad \mu_{k}\quad (t)}} \right)}\quad t} \in {{noise}\quad {period}}}$

where A_(k)(t) is said adaptive attenuation coefficient for a frequencyindex k at a frame t, A is said attenuation coefficient, α is saidoverestimation coefficient, μ_(k)(t) is said noise average for frequencyindex k at frame t, Sp_(k)(t) is a noisy speech average for frequencyindex k at frame t, μ_(k)(prev) is a noise average for a noise periodimmediately previous to a current utterance, and Sp_(k)(prev) is a noisyspeech average for an utterance immediately previous to a current noiseperiod.
 21. The method of claim 20, wherein said noise suppressorcalculates said noisy speech average according to a formula: Sp_(k)(t)=ySp_(k)(t−1)+(1−y)Y _(k)(t) where Sp_(k)(t) is said noisy speechaverage for frequency index k at frame t, Y_(k)(t) is a noisy speechamplitude energy value for frequency index k at frame t, and y is aspeech forgetting coefficient.
 22. The method of claim 15, wherein saidnoise suppressor determines a noise average and a noise standarddeviation of said energy amplitude values of said noise signal, utilizessaid noise average and said noise standard deviation to identifyselected ones of said amplitude energy values of said noisy speechsignal that have a probability of containing noise, and selectivelyattenuates said amplitude energy values of said noisy speech signalaccording to said probability.
 23. The method of claim 15, wherein saidnoise suppressor calculates said noise average according to a formula:$\mu_{k} = {\frac{1}{T}\quad {\sum\limits_{t = 1}^{T}\quad {N_{k}\quad (t)}}}$

where μ_(k) is said noise average for a frequency index k, N_(k)(t) is anoise energy amplitude value for frequency index k at a frame t for tequal to 1 through T, and T is a total number of frames in a noiseperiod.
 24. The method of claim 23, wherein said noise suppressorcalculates said noise standard deviation according to a formula:$\sigma_{k} = \sqrt{\frac{1}{T}\quad {\sum\limits_{t = 1}^{T}\quad \left( {{N_{k}\quad (t)} - \mu_{k}} \right)^{2}}}$

where σ_(k) is said noise standard deviation for frequency index k,μ_(k) is said noise average for frequency index k, N_(k)(t) is saidnoise energy amplitude value for frequency index k at said frame t for tequal to 1 through T, and T is said total number of frames in said noiseperiod.
 25. The method of claim 15, further comprising the step ofgenerating amplitude energy values of said noisy speech signal using aFast Fourier transformer.
 26. The method of claim 25, further comprisingthe steps of providing attenuated noisy speech amplitude energy valuesto a filter bank, and generating channel energies using said filterbank.
 27. The method of claim 26, further comprising the step ofconverting said channel energies into logarithmic channel energies usinga logarithmic compressor.
 28. The method of claim 27, further comprisingthe step of converting said logarithmic channel energies intocorresponding static features using a frequency cosine transformer. 29.The method of claim 28, further comprising the step of providing saidcorresponding static features to a normalizer, a first cosinetransformer, and a second cosine transformer.
 30. The method of claim29, further comprising the steps of converting said corresponding staticfeatures into delta features using said first cosine transformer,converting said corresponding static features into delta-delta featuresusing said second cosine transformer, and providing said delta featuresand said delta-delta features to said normalizer.
 31. The method ofclaim 30, further comprising the step of normalizing said staticfeatures, said delta features, and said delta-delta features using saidnormalizer to produce normalized static features, normalized deltafeatures, and normalized delta-delta features.
 32. The method of claim31, further comprising the step of analyzing said normalized staticfeatures, said normalized delta features, and said normalizeddelta-delta features using a recognizer to produce a speech recognitionresult.
 33. A method for noise attenuation in an electronic system,comprising the steps of: selectively attenuating additive noise in anelectronic signal using a noise suppressor, said electronic signal beinga noisy speech signal that includes a noise signal combined with aspeech signal, said noise suppressor selectively attenuating said noisesignal by utilizing statistical characteristics of amplitude energyvalues of said noise signal, said statistical characteristics of saidamplitude energy values of said noise signal include a noise average anda noise standard deviation, said noise suppressor generating anattenuated noisy speech signal according to a formula: $\begin{matrix}{{Yat}_{k} = \frac{Y_{k}}{1 + A_{}^{{- \frac{1}{2}}\quad {(\frac{Y_{k} - {({\mu_{k} + {\alpha_{v}\quad \sigma_{k}}})}}{\sigma_{k}})}^{2}}}} & {{{if}\quad Y_{k}} > {\mu_{k} + {\alpha_{v}\quad \sigma_{k}}}} \\{{Yat}_{k} = \frac{Y_{k}}{1 + A}} & {otherwise}\end{matrix}$

 where Yat_(k) is said attenuated noisy speech signal for a frequency k,Y_(k) is said noisy speech signal for said frequency k, μ_(k) is saidnoise average for said frequency k, σ_(k) is said noise standarddeviation for said frequency k, α_(v) is an overestimation coefficientrelated to said noise standard deviation, and A is an attenuationcoefficient; and controlling said noise suppressor with a processorcoupled to said electronic system.
 34. A method for noise attenuation inan electronic system, comprising the steps of: selectively attenuatingadditive noise in an electronic signal using a noise suppressor, saidelectronic signal being a noisy speech signal that includes a noisesignal combined with a speech signal, said noise suppressor selectivelyattenuating said noise signal by utilizing statistical characteristicsof amplitude energy values of said noise signal, said statisticalcharacteristics of said amplitude energy values of said noise signalinclude a noise average and a noise standard deviation, said noisesuppressor calculating said noise average according to a formula:μ_(k)(t)=βμ_(k)(t−1)+(1−β)N _(k)(t)  where μ_(k)(t) is said noiseaverage for a frequency index k at a frame t, N_(k)(t) is a noise energyamplitude value for frequency index k at frame t, and β is a noiseforgetting coefficient; and controlling said noise suppressor with aprocessor coupled to said electronic system.
 35. The method of claim 34,wherein said noise suppressor calculates a noise second moment accordingto a formula: S _(k)(t)=βS _(k)(t−1)+(1−β)N _(k)(t)N _(k)(t) whereS_(k)(t) is said noise second moment for frequency index k at frame t,N_(k)(t) is said noise energy amplitude value for frequency index k atframe t, and β is said noise forgetting coefficient.
 36. The method ofclaim 35, wherein said noise suppressor calculates said noise standarddeviation according to a formula: σ_(k)(t)={square root over (S_(k)(t)−μ_(k)(t)μ_(k)(t))} where σ_(k)(t) is noise standard deviationfor frequency index k at frame t, S_(k)(t) is said noise second momentfor frequency index k at frame t, and μ_(k)(t) is said noise average forfrequency index k at frame t.
 37. An apparatus for noise attenuation inan electronic system, comprising: a noise suppressor configured toselectively attenuate additive noise in an electronic signal, said noisesuppressor determining a noise average and a noise standard deviation ofenergy amplitude values of a noisy speech signal, said noise suppressorutilizing said noise average and said noise standard deviation toidentify said amplitude energy values of said noisy speech signal thathave a statistical probability of containing said additive noise, saidnoise suppressor selectively attenuating said amplitude energy values ofsaid noisy speech signal according to said statistical probability, saidnoise suppressor calculating said noise average according to a formula:μ_(k)(t)=βμ_(k)(t−1)+(1−β)N _(k)(t)  where μ_(k)(t) is said noiseaverage for a frequency index k at a frame t, N_(k)(t) is a noise energyamplitude value for frequency index k at frame t, and β is a noiseforgetting coefficient; and a processor coupled to said electronicsystem to control said noise suppressor.
 38. The apparatus of claim 37,wherein said noise suppressor calculates a noise second moment accordingto a formula: S _(k)(t)=βS _(k)(t−1)+(1−β)N _(k)(t)N _(k)(t) whereS_(k)(t) is said noise second moment for frequency index k at frame t,N_(k)(t) is said noise energy amplitude value for frequency index k atframe t, and β is said noise forgetting coefficient.
 39. The apparatusof claim 38, wherein said noise suppressor calculates said noisestandard deviation according to a formula: σ_(k)(t)={square root over (S_(k)(t)−μ_(k)(t)μ_(k)(t))} where σ_(k)(t) is said noise standarddeviation for frequency index k at frame t, S_(k)(t) is noise secondmoment for frequency index k at frame t, and μ_(k)(t) is said noise ragefor frequency index k at frame t.